Invariants
Level: | $88$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}37&40\\16&47\end{bmatrix}$, $\begin{bmatrix}41&40\\50&73\end{bmatrix}$, $\begin{bmatrix}61&32\\22&81\end{bmatrix}$, $\begin{bmatrix}81&48\\42&45\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.48.0.bb.2 for the level structure with $-I$) |
Cyclic 88-isogeny field degree: | $12$ |
Cyclic 88-torsion field degree: | $480$ |
Full 88-torsion field degree: | $211200$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
88.48.0-8.i.1.2 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.i.2.3 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.i.2.5 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.bv.2.5 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.bv.2.12 | $88$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
88.192.1-88.q.2.7 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.br.2.3 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.cc.2.4 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.cg.2.3 | $88$ | $2$ | $2$ | $1$ |
176.192.1-176.c.1.4 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.l.1.2 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.o.1.4 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.r.1.2 | $176$ | $2$ | $2$ | $1$ |
176.192.3-176.bq.2.11 | $176$ | $2$ | $2$ | $3$ |
176.192.3-176.bv.2.9 | $176$ | $2$ | $2$ | $3$ |
176.192.3-176.ce.2.11 | $176$ | $2$ | $2$ | $3$ |
176.192.3-176.co.2.9 | $176$ | $2$ | $2$ | $3$ |
264.192.1-264.kz.2.3 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ld.2.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.pv.1.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.qd.1.2 | $264$ | $2$ | $2$ | $1$ |
264.288.8-264.pm.1.41 | $264$ | $3$ | $3$ | $8$ |
264.384.7-264.jt.1.17 | $264$ | $4$ | $4$ | $7$ |